{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T16:21:38Z","timestamp":1775838098826,"version":"3.50.1"},"reference-count":34,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,9,7]],"date-time":"2023-09-07T00:00:00Z","timestamp":1694044800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"NATIONAL RESEARCH FOUNDATION South Africa","award":["98398"],"award-info":[{"award-number":["98398"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>The electrical energy demand increase does evolve rapidly due to several socioeconomic factors such as industrialisation, population growth, urbanisation and, of course, the evolution of modern technologies in this 4th industrial revolution era. Such a rapid increase in energy demand introduces a huge challenge into the power system, which has paved way for network operators to seek alternative energy resources other than the conventional fossil fuel system. Hence, the penetration of renewable energy into the electricity supply mix has evolved rapidly in the past three decades. However, the grid system has to be well planned ahead to accommodate such an increase in energy demand in the long run. Transmission Network Expansion Planning (TNEP) is a well ordered and profitable expansion of power facilities that meets the expected electric energy demand with an allowable degree of reliability. This paper proposes a DC TNEP model that minimises the capital costs of additional transmission lines, network reinforcements, generator operation costs and the costs of renewable energy penetration, while satisfying the increase in demand. The problem is formulated as a mixed integer linear programming (MILP) problem. The developed model was tested in several IEEE test systems in multi-period scenarios. We also carried out a detailed derivation of the new non-negative variables in terms of the power flow magnitudes, the bus voltage phase angles and the lines\u2019 phase angles for proper mixed integer variable decomposition techniques. Moreover, we intend to provide additional recommendations in terms of in which particular year (within a 20 year planning period) can the network operators install new line(s), new corridor(s) and\/or additional generation capacity to the respective existing power networks. This is achieved by running incremental period simulations from the base year through the planning horizon. The results show the efficacy of the developed model in solving the TNEP problem with a reduced and acceptable computation time, even for large power grid system.<\/jats:p>","DOI":"10.3390\/computation11090179","type":"journal-article","created":{"date-parts":[[2023,9,7]],"date-time":"2023-09-07T09:56:36Z","timestamp":1694080596000},"page":"179","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["The Efficacy of Multi-Period Long-Term Power Transmission Network Expansion Model with Penetration of Renewable Sources"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6100-7826","authenticated-orcid":false,"given":"Gideon Ude","family":"Nnachi","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering, Faculty of Engineering and the Built Environment, Tshwane University of Technology Pretoria Campus, Pretoria 0001, South Africa"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9673-9189","authenticated-orcid":false,"given":"Yskandar","family":"Hamam","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Faculty of Engineering and the Built Environment, Tshwane University of Technology Pretoria Campus, Pretoria 0001, South Africa"}]},{"given":"Coneth Graham","family":"Richards","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Faculty of Engineering and the Built Environment, Tshwane University of Technology Pretoria Campus, Pretoria 0001, South Africa"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"320","DOI":"10.1016\/j.ijepes.2018.02.024","article-title":"Candidate line selection for transmission expansion planning considering long-and short-term uncertainty","volume":"100","author":"Zhang","year":"2018","journal-title":"Int. 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